Calculate the resistance of a piece of aluminum wire with a diameter of 100 mils and a length of two miles, at 68°F. Hint: Be sure to first convert mils to cmils and use the K value for aluminum found in the reference. (Round the FINAL answer to two decimal places.)
First you need to know the formula of the Resistance(R) of a conductor, which is:
[tex]R = \frac{K*L}{CM} [/tex] -- (A)
Where, R = Resistance of the wire = ? K = Specific resistance of the wire(In this case Aluminum at 68°F) = 17.02 ohm-circular-mil-foot L = Length of the wire(in feet) CM = Circular mil Area(In inches)
Now in order to use the above formula(A), we have to first convert TWO quantities: 1) The length of the wire(from miles to feet) 2) Mils to Circular mil Area
1. The length of the wire given = 2 miles The length of the wire(In feet) = 10560 ft 2. Since the mils given = 100 mils. Therefore, Circular mils(Circular mil Area) = mils x mils = 100 x 100 = 10000
Now plug-in the values in equation(A):
A=> R = [tex]\frac{17.02 * 10560}{10000 } [/tex]
R = 17.97 ohms
Ans: Resistance of the aluminum wire = 17.97 ohms.
